Dormer could have solved his sleeplessness in many ways: Requesting another room (with blackout shades), put foil over the window, move his head to the foot end of the bed, find a place at the police station to sleep, and take off street clothes before lying down to sleep.
At the beginning, when Ellie Burr is telling Dormer how she knows about his past cases, she asks if the scar on his neck is where Ronald Langley cut him during the Leland Street Murders case, but then immediately says that the Leland Street Murders were her case study at the academy. If so, she should have known that that was where he was cut. (This could be attributed to the character's nervousness at meeting Dormer.)
Photo of Walter that Will picks up from Walters house remains dry despite the fact that Will fell into the water when chasing across the logs. There are no signs of the fact that it got wet when it is next shown.
The dead dog in the alley has been dead for quite some time. When
Dormer uses the gun, then digs out the spent bullet the dog's blood and flesh seem very bright and fresh. The blood would have coagulated and the buzzing flies indicate that the flesh had begun to deteriorate, thus giving off an odor.
When Ellie Burr asks Dormer to sign the report and Dormer tells her to be sure of all of her facts, he walks out of shot having taken his glasses off. In the next brief shot of him passing by so we can see Ellie's reaction, his glasses are back on his face.
When Dormer first enters Finch's apartment, he picks the lock using a credit card. After the door is open, we see him getting his hand back to his pocket and in the next shot he has some snacks in his hand to bribe the dogs to let him in. Since his hand motion is very quick and brief, it either serves to get the snacks from the pocket, in which case the credit card simply disappears, or to get the card back to the pocket, in which case the snacks materialize out of nowhere.
Dormer, a seasoned police detective who demonstrates in the story that he understands the properties of blood, including DNA and proteins, chooses to use hot water to clean the blood off his clothes (you can see the hot water tap is wide open and the cold tap is closed in the sink in his hotel room). Hot water binds blood to clothes and makes a permanent stain. Cold water removes blood.
The information regarding Glock pistols is incorrect. The slide, while it is steel, does not have a blued finish. The finish is called Tenifer, and is proprietary to Glock. The Tenifer makes the slide essentially rust proof. The only parts that may have a tendency to rust are the sights which have a different finish. Gun enthusiasts often refer to the Glock as "dishwasher safe".
In the initial shots of the Beech 18 seaplane, when supposedly cruising to destination, the aircraft is clearly flying too low and has one notch of flaps down. This is not a normal cruise flight configuration.
When the police officers are waiting for the murderer to return to the cabin for the girl's backpack (Scene 8 on the DVD), they are talking about firearms. One of the Alaska cops says "Yeah that's nice, mine's all plastic save the barrel and firing pin - never rusts. What do you carry down in LA?" In the real world, the only part on his Glock that is plastic is the frame. The barrel, firing pin, trigger components, and SLIDE are all metal. Seeing how the Glock's frame (that's the big part on top) is 100% blued metal, it rusts just as easily as anything else.
Dorner displays abysmal handling of his service weapon, consistently violating the third of Cooper's four famous gun safety rules ("Keep your finger off the trigger till your sights are on the target."). What's more, the death of his partner is a direct result of Dorner violating the fourth rule ("Identify your target, and what is behind it. Never shoot at anything that you have not positively identified.") Given his age, it is possible that Dorner went to police academy before it was common for law enforcement agencies to require their staff to comply with Cooper's rules (i.e. before around 1985). That the young Burr, who leads the investigation of the incident, would neither mention Dorner's outrageous violations nor try to find out whether he had received updated weapons training is, however, utterly impossible.
The comment about Walter's trigger finger position is partially correct. A double barrel shotgun usually has two triggers, one behind the other and one for each barrel. It's reasonable that an open trigger would be visible while firing with the second trigger.
On the ferry, the Pacino character and the Williams character have a long discussion. Outside the window of the ferry the foreshore scenery does not move, yet they are supposed to be sailing somewhere.
When Walter falls into the water though the bottom of the boat house at the end of the movie he falls about 1 foot before he hits the water. In the next scene when Detective Ellie is leaving the boat house the water is 5 or 6 feet below the bottom of the boat house.